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Chapter 4: Problem 80

Evaluate the square roots. $$\sqrt{\frac{1}{100}}$$

Short Answer

Expert verified
0.1

Step by step solution

01

Rewrite the Fraction

Rewrite the fraction inside the square root. The fraction \(\frac{1}{100}\) can be expressed as \(1 \text{ divided by } 100\).
02

Simplify the Fraction

Rewrite the fraction under the square root as \(\frac{1}{10^2}\). This makes it easier to apply the square root.
03

Apply the Square Root Property

Use the property of square roots that \(\frac{1}{a^2} = \frac{1}{a}\). For \(a = 10\), this gives \(\sqrt{\frac{1}{100}} = \frac{1}{10}\).
04

Simplify the Result

Simplify the result to get \(\frac{1}{10} = 0.1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fractions
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). In our exercise, the fraction is \(\frac{1}{100}\).
\(\frac{1}{100}\) means 1 out of 100 parts. Understanding fractions is key to simplifying and evaluating square roots.
When working with square roots and fractions, it helps to express the fraction in its simplest form.
Square Root Property
The square root property simplifies expressions involving square roots. The general rule is \(\frac{1}{a^2} = \frac{1}{a}\).
This property helps to break down the fraction under the square root into a more manageable number.
For instance, \(a = 10\) in our exercise, so \(\frac{1}{10^2}\) becomes \(\frac{1}{10}\) after applying the square root.
Without this property, simplifying complex expressions would be difficult.
Simplification
Simplification is the process of making an equation or expression easier to work with.
In our case, simplifying \(\frac{1}{100}\) under the square root involves reducing it to \(\frac{1}{10}\).
We then convert this fraction to a decimal, giving us 0.1. This step is important to clear any confusion and present the answer neatly.
Simplifying fractions and square roots makes problems easier to solve and understand.

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Most popular questions from this chapter

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